Several cargo trucks entered the Nepali side from Sunauli border in Bhairahawa.
More than 300 trucks carrying essential supplies have been stranded on the Indian side due to the ongoing blockade imposed the Madhesi groups opposing the promulgation of the new Constitution.
Madhesis are Indian-origin inhabitants of the Terai region bordering India who are opposed to splitting Nepal into seven provinces.
At least 40 people have died in over a month of clashes between police and protesters from the Madhesi and Tharu communities and ethnic minorities.
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The blockade in the Nepal-India border point has made life harder for the people of Nepal for the past 4-5 days.
Some people in Nepal blame India for the shortage by imposing an embargo.
India denies imposing blockade, saying truck drivers are concerned for their safety after protests in the country.